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A347974
Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_8)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).
2
1, 1, 1, 1, 5, 1, 1, 17, 17, 1, 1, 47, 242, 47, 1, 1, 113, 3071, 3071, 113, 1, 1, 245, 34477, 232290, 34477, 245, 1, 1, 491, 341633, 16665755, 16665755, 341633, 491, 1, 1, 920, 3022045, 1073874283, 8241549097, 1073874283, 3022045, 920, 1, 1, 1635, 24145695
OFFSET
0,5
COMMENTS
Columns can be computed by a method analogous to that of Fripertinger for isometry classes of linear codes, disallowing scalar transformation of individual coordinates.
Regarding the formula for column k = 1, note that A241926(q - 1, n) counts, up to coordinate permutation, one-dimensional subspaces of (F_q)^n generated by a vector with no zero component.
LINKS
H. Fripertinger, Isometry classes of codes
FORMULA
T(n, 1) = T(n - 1, 1) + A032192(n + 7).
EXAMPLE
Triangle begins:
k: 0 1 2 3 4 5
--------------------------
n=0: 1
n=1: 1 1
n=2: 1 5 1
n=3: 1 17 17 1
n=4: 1 47 242 47 1
n=5: 1 113 3071 3071 113 1
There are 9 = A022172(2, 1) one-dimensional subspaces in (F_8)^2. Among them, <(1, 1)> is invariant by coordinate swap and the rest are grouped in orbits of size two. Hence, T(2, 1) = 5.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Álvar Ibeas, Sep 21 2021
STATUS
approved